Which of the following pairs of variables is likely to have a negative correlation? Select all that apply.
a. The number of miles run and the number of calories burned
b. A person's height and their favorite color
c. The speed of a car and the time to its destination
d. Years of education and salary
c. The square footage of a home and its price
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The pairs of variables that are likely to have a negative correlation are:
a. The number of miles run and the number of calories burned
c. The speed of a car and the time to its destination
d. Years of education and salary
To determine which pairs of variables is likely to have a negative correlation, we need to understand what a negative correlation means. In statistics, a negative correlation between two variables means that as one variable increases, the other variable tends to decrease.
Let's analyze each pair of variables:
a. The number of miles run and the number of calories burned: In general, as the number of miles run increases, the number of calories burned also increases. This indicates a positive correlation rather than a negative correlation. Therefore, this pair of variables does not have a negative correlation.
b. A person's height and their favorite color: There is no inherent relationship or logical connection between a person's height and their favorite color. Hence, these variables are likely to be independent of each other. As a result, we cannot determine any correlation between them.
c. The speed of a car and the time to its destination: As the speed of a car increases, the time it takes to reach the destination decreases. This indicates a negative correlation. Therefore, this pair of variables is likely to have a negative correlation.
d. Years of education and salary: Typically, as the level of education (measured in years) increases, a person's salary tends to increase as well. This implies a positive correlation rather than a negative correlation. Hence, this pair of variables does not have a negative correlation.
e. The square footage of a home and its price: In general, as the square footage of a home increases, its price also increases. This implies a positive correlation instead of a negative correlation. Therefore, this pair of variables does not have a negative correlation.
Based on our analysis, the pair of variables that is likely to have a negative correlation is c. The speed of a car and the time to its destination.